The p-adic Hayman conjecture when n = 2 Article - 2014

Alain Escassut, Jacqueline Ojeda

Alain Escassut, Jacqueline Ojeda, « The p-adic Hayman conjecture when n = 2  », Complex Variables and Elliptic Equations, 2014. ISSN 1747-6933

Abstract

Let IK be a complete ultrametric algebraically closed field of characteristic 0. According to the p-adic Hayman conjecture, given a transcendental meromorphic function f in IK, for each n ∈ IN * , f n f takes every value b = 0 infinitely many times. It was proven by the second author for n ≥ 3. Here we prove it for n = 2 by using properties of meromorphic functions having finitely many multiple poles. .

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